In the past few years, browsers have been changing some aspects of how they deal with pages accessed via https:// that include resources that are referenced with simply http, which technically means the connection is not secure. They originally would just indicate to the user that the connection was insecure and trudge on regardless. More recently, browsers will sometimes display a special warning page and wait for the user to decide whether or not to continue. I hadn't heard of any browser simply omitting resources that aren't accessed securely, but I could understand if that's what Firefox has done.
In this case, it sounds like the custom font is referenced in the stylesheet with an http URL and so Firefox is refusing to load it. If so, one fix would be to change the stylesheet so that it uses a relative URL to point to the font file. Or you could set the page to use a separate stylesheet which uses https in the URL for the font file. In any case, I think you need to fix the problem even if its only Firefox that seems to have an issue because it could just be the first of several you'll find as your testing proceeds to the checkout process.